Download energy diagrams

Physics 218: Mechanics
Instructor: Dr. Tatiana Erukhimova
Lecture 24
Water Slide
Who will come first?
The curve of fastest descent
Cycloid
Inverted cycloid:
Brachistochrone
http://curvebank.calstatela.edu/brach/brach.htm
ENERGY DIAGRAMS
Potential Energy Diagrams
• For Conservative
forces can draw
energy diagrams
• Equilibrium points
– Motion will move
“around” the
equilibrium
– If placed there with
no energy, will just
stay (no force)
Fx  
dU
dx
0
Stable vs. Unstable Equilibrium
Points
The force is zero at both maxima and minima
but…
– If I put a ball with no velocity there would it stay?
– What if it had a little bit of velocity?
A particle moves along the x-axis while acted
on by a single conservative force parallel to
the x-axis. The force corresponds to the
potential-energy function graphed in the
Figure. The particle is released from rest at
point A.
a)What is the direction of the force on the
particle when it is at point A?
b) At point B?
c) At what value of x is the kinetic energy of the
particle a maximum?
d) What is the force on the particle when it is at
point C?
e) What is the largest value of x reached by the
particle during its motion?
f) What value or values of x correspond to points
of stable equilibrium?
g) Of unstable equilibrium?
Quiz
Quiz
A block of mass m is attached to a vertical spring,
spring constant k. The spring is unstretched at y=0.
A
If the spring is compressed an amount A and the block
released from rest, how high will it go?